Related papers: Reducing Sensor Requirements by Relaxing the Netwo…
The threshold-$k$ metric dimension ($\mathrm{Tmd}_k$) of a graph is the minimum number of sensors -- a subset of the vertex set -- needed to uniquely identify any vertex in the graph, solely based on its distances from the sensors, when the…
A Semidefinite Programming (SDP) relaxation is an effective computational method to solve a Sensor Network Localization problem, which attempts to determine the locations of a group of sensors given the distances between some of them [11].…
The metric dimension of a graph is the smallest number of nodes required to identify all other nodes based on shortest path distances uniquely. Applications of metric dimension include discovering the source of a spread in a network,…
Locating source of diffusion in networks is crucial for controlling and preventing epidemic risks. It has been studied under various probabilistic models. In this paper, we study source location from a deterministic point of view by…
This manuscript is a preliminary pre-print version of a journal submission by the authors, revisiting the problem of range measurement based localization of a signal source or a sensor. The major geometric difficulty of the problem comes…
We consider the sensor network localization problem, which is closely related to multidimensional scaling and Euclidean distance matrix completion. Given a ground truth configuration of $n$ points in $\mathbb{R}^\ell$, we observe a subset…
One important problem in a network is to locate an (invisible) moving entity by using distance-detectors placed at strategical locations. For instance, the metric dimension of a graph $G$ is the minimum number $k$ of detectors placed in…
The metric dimension of a graph is the minimum number of landmark vertices required so that every vertex can be uniquely identified by its distances to the landmarks. This parameter captures the fundamental tradeoff between compact…
A recent research direction in data-driven modeling is the identification of dynamic networks, in which measured vertex signals are interconnected by dynamic edges represented by causal linear transfer functions. The major question…
The metric dimension, $\dim(G)$, of a graph $G$ is a graph parameter motivated by robot navigation that has been studied extensively. Let $G$ be a graph with vertex set $V(G)$, and let $d(x,y)$ denote the length of a shortest $x-y$ path in…
Locating sources of diffusion and spreading from minimum data is a significant problem in network science with great applied values to the society. However, a general theoretical framework dealing with optimal source localization is…
The metric dimension of a graph G is the minimum size of a subset S of vertices of G such that all other vertices are uniquely determined by their distances to the vertices in S. In this paper we investigate the metric dimension for two…
The notion of resolving sets in a graph was introduced by Slater (1975) and Harary and Melter (1976) as a way of uniquely identifying every vertex in a graph. A set of vertices in a graph is a resolving set if for any pair of vertices x and…
This paper studies a graph-based sensor deployment approach in wireless sensor networks (WSNs). Specifically, in today's world, where sensors are everywhere, detecting various attributes like temperature and movement, their deteriorating…
A vertex $v\in V$ is said to resolve two vertices $x$ and $y$ if $d_G(v,x)\ne d_G(v,y)$. A set $S\subset V$ is said to be a metric generator for $G$ if any pair of vertices of $G$ is resolved by some element of $S$. A minimum metric…
In a network consisting of n nodes, our goal is to identify the most central k nodes with respect to the proposed definitions of centrality. Depending on the specific application, there exist several metrics for quantifying k-centrality,…
The metric dimension of a graph is the minimum size of a set of vertices such that each vertex is uniquely determined by the distances to the vertices of that set. Our aim is to upper-bound the order $n$ of a graph in terms of its diameter…
The metric dimension of a graph is the cardinality of a minimum resolving set, which is the set of vertices such that the distance representations of every vertex with respect to that set are unique. A fault-tolerant metric basis is a…
The classical (vertex) metric dimension of a graph G is defined as the cardinality of a smallest set S in V (G) such that any two vertices x and y from G have different distances to least one vertex from S: The k-metric dimension is a…
Information diffusion in networks can be used to model many real-world phenomena, including rumor spreading on online social networks, epidemics in human beings, and malware on the Internet. Informally speaking, the source localization…